Geometry Word Problems

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Question 1 of 2

The perimeter of the plot of land below is

98

$98$ m

(i)

$(i)$ What is the length and width of the land?

(i i)

$(ii)$ What is the area of the land?

$(i)$ $(i)$ length: (28) $m$ $\text(m)$ , width: (21) $m$ $\text(m)$

$(i i)$ $(ii)$ Area: (588) $m^{2}$ $\text(m)^2$

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A word problem can be translated into an equation for easier solving.

Perimeter of a Rectangle

P = 2 l + 2 w

$P=2l+2w$

Area of a Rectangle

A = l w

$A=lw$

(i)

$(i)$ Find the length and width of the land.

Slot in the given values into the Perimeter Formula to form an equation

P = 98

$P=98$

l = x + 7

$l=x+7$

w = x

$w=x$

$P$ $P$	$=$ $=$	$2 l + 2 w$ $2l+2w$	Perimeter Formula
$98$ $98$	$=$ $=$	$2 (x + 7) + 2 (x)$ $2(x+7)+2(x)$

Solve for

x

$x$

$98$ $98$	$=$ $=$	$2 (x + 7) + 2 (x)$ $2(x+7)+2(x)$
$98$ $98$	$=$ $=$	$2 x + 14 + 2 x$ $2x+14+2x$
$98$ $98$	$=$ $=$	$4 x + 14$ $4x+14$
$4 x + 14$ $4x+14$	$=$ $=$	$98$ $98$
$4 x + 14$ $4x+14$ $- 14$ $-14$	$=$ $=$	$98$ $98$ $- 14$ $-14$	Subtract $14$ $14$ from both sides
$4 x$ $4x$	$=$ $=$	$84$ $84$
$4 x$ $4x$ $\div 4$ $-:4$	$=$ $=$	$84$ $84$ $\div 4$ $-:4$	Divide both sides by $4$ $4$
$x$ $x$	$=$ $=$	$21$ $21$ m	width of the land

Solve for

x + 7

$x+7$

	$x + 7$ $x+7$
$=$ $=$	$21 + 7$ $21+7$	Substitute $x$ $x$
$=$ $=$	$28$ $28$ m	length of the land

(i i)

$(ii)$ Find the area of the land.

Slot in the values from part

(i)

$(i)$ into the Area Formula

l = 28

$l=28$ m

w = 21

$w=21$ m

$A$ $A$	$=$ $=$	$l w$ $lw$	Area Formula
	$=$ $=$	$(28) (21)$ $(28)(21)$
	$=$ $=$	$588 m^{2}$ $588\text(m)^2$

(i)

$(i)$ length:

28

$28$ m, width:

21

$21$ m

(i i)

$(ii)$ Area:

588 m^{2}

$588\text(m)^2$

Question 2 of 2

Find the size of each angle in this triangle:

$3 x =$ $3x=$ (51) $°$ $°$

$3 x + 12 =$ $3x+12=$ (63) $°$ $°$

$4 x - 2 =$ $4x-2=$ (66) $°$ $°$

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A word problem can be translated into an equation for easier solving.

Form an equation using the values given

Remember that the sum of all interior angles in a triangle is

180 °

$180°$

Angle

1

$1$ :

3 x

$3x$

Angle

2

$2$ :

3 x + 12

$3x+12$

Angle

3

$3$ :

4 x - 2

$4x-2$

Angle $1 +$ $1+$ Angle $2 +$ $2+$ Angle $3$ $3$	$=$ $=$	$180 °$ $180°$
$3 x + (3 x + 12) + (4 x - 2)$ $3x+(3x+12)+(4x-2)$	$=$ $=$	$180 °$ $180°$

Solve for

x

$x$

$3 x + (3 x + 12) + (4 x - 2)$ $3x+(3x+12)+(4x-2)$	$=$ $=$	$180 °$ $180°$
$10 x + 10$ $10x+10$	$=$ $=$	$180$ $180$
$10 x + 10$ $10x+10$ $- 10$ $-10$	$=$ $=$	$180$ $180$ $- 10$ $-10$	Subtract $10$ $10$ from both sides
$10 x$ $10x$	$=$ $=$	$170$ $170$
$10 x$ $10x$ $\div 10$ $-:10$	$=$ $=$	$170$ $170$ $\div 10$ $-:10$	Divide both sides by $10$ $10$
$x$ $x$	$=$ $=$	$17$ $17$

Solve for the size of each angle

Angle

1

$1$ :

		$3 x$ $3x$
	$=$ $=$	$3 (17)$ $3(17)$
	$=$ $=$	$51 °$ $51°$

Angle

2

$2$ :

		$3 x + 12$ $3x+12$
	$=$ $=$	$3 (17) + 12$ $3(17)+12$
	$=$ $=$	$51 + 12$ $51+12$
	$=$ $=$	$63 °$ $63°$

Angle

3

$3$ :

		$4 x - 2$ $4x-2$
	$=$ $=$	$4 (17) - 2$ $4(17)-2$
	$=$ $=$	$68 - 2$ $68-2$
	$=$ $=$	$66 °$ $66°$

Angle

1

$1$ :

51 °

$51°$

Angle

2

$2$ :

63 °

$63°$

Angle

3

$3$ :

66 °

$66°$

Geometry Word Problems

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Quiz summary

Information

1. Question

Hint

Excellent!

Perimeter of a Rectangle

Area of a Rectangle

2. Question

Hint

Well Done!

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