Question

The height of a triangle is twice the length of its base. The area of the triangle is 50 m2. Find the height and base to the nearest tenth of a meter.

Answer 1

Base = 7.1m

Height = 14.2m

Explanation:

Let's take the base as 'x'.

And the height is twice the base so it is 2 × x which is 2x.

Then, the formula for finding area of a triangle is:

Area of a triangle =
`(1)/(2)` × base × height

From this equation we will be able to find the value of 'x'.

The area is 50
`m^(2)`. Now substitute all the terms into the equation.

50 =
`(1)/(2)` × x × 2x

50 =
`(1)/(2)` ×
`2x^(2)`

50 =
`(2x^(2) )/(2)`

The '2' in the numerator and denominator can be cut off.

`x^(2)` = 50

x =
`√(50)`

x = 7.07 = 7.1m ( to the nearest tenth )

So when the base is 7.07 the height, as mentioned, is twice of base, 2x. We have the value of x so just substitute the value of x in 2x.

2 × 7.1 = 14.2m

Answer 2

Explanation:

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