Question

The area of
this triangle
is 180 ft?,
what does x
have to be?

Answer 1

x has to be 6

Explanation:

Let us revise the rule of the area of a triangle

→ The area of any triangle =
`(1)/(2)` × base × height

In the given triangle:

∵ The triangle is a right triangle

∵ Its base = 5x ft

∵ Its height = 12 ft

∵ Its area = 180 ft²

→ Substitute these values in the rule of the area above

∴ 180 =
`(1)/(2)` × 5x × 12

→ Simplify the right side

∵
`(1)/(2)` × 5x × 12 = 30x

∴ 180 = 30x

→ Divide both sides by 30 to find x

∴
`(180)/(30)=(30x)/(30)`

∴ 6 = x

∴ x has to be 6

To check your answer find the area of the triangle

∵ Its base = 5x = 5(6) = 30 ft

∵ Its height = 12 ft

∴ Its area =
`(1)/(2)` × 30 × 12 180 ft²

∴ The value of x is correct.