Question

the base and height of a triangle are in the ratio 7:4 if the area of the triangle is 87.5 CM then it's base and height

Answer 1

Hi there!

Here's your answer


let the common factor be x

base = 7x

height = 4x

$area \: of \: triangle \: = \frac{1}{2} \times b \times h$
where b is base and h is the height


$\frac{875}{10} = \frac{1}{2} \times 7x \times 4x$


$\frac{875 \times 2}{10} = 28 {x}^{2}$

$175 = 28 {x}^{2}$

${x}^{2} = \frac{175}{28}$

${x}^{2} = 6.25$

$x = \sqrt{6.25}$

$x = 2.5$


base = 7x = 7 × 2.5 = 17.5cm

altitude = 4x = 4 × 2.5 = 10cm

Answer 2

Let the ratio be in x
Therefore, base =7x
Height =4x
Area =87.5cm
According to the question,
Area =1/2×b×h
=1/2×7x×4x=87.5cm
=28x2=87.5×2
=x2=87.5×2/28
=x=2.5cm
Base =7×2.5=17.5cm
Height=4×2.5=10cm