Question

the base and height of a triangle are in the ratio 4:5 if the area of a triangle is 90 square metres find the measure of its base and height ​

Answer 1

Step-by-step explanation:

Let its base and height are 4x and 5x respectively.

area of triangle = 90 sq meters.

$= > (1 \div 2) \times 4x \times 5x = 90 \\ = > {x}^{2} = (90 \times 2) \div 20 \\ = > {x}^{2} = 9 \\ x = \sqrt{9} \\ = > x = + 3 \: \: \: or \: - 3$

So, it's base = 4×3 = 12 and height = 5x = 5×3 = 15

respectively.

Answer 2

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Base and height are in ratio 4:5.

• Area of triangle is 90m².

$\\ \\ \large\underline{ \underline{ \sf{ \red{ to \:fi nd:} }}}$

• Base and height.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Let base be '4x' and height be '5x' as ratio is 4:5.

$\\ \small\bigstar\boxed{ \bf \: area \: of \: triangle = \frac{1}{2} \times base \times height }$

We have ,

• Area of triangle = 90m².

• Base = 4x

• Height = 5x

Putting values , we get..

$\\ \sf \: 90 = \frac{1}{2} \times (4x) \: (5x) \\ \\ \sf \: 90 \times 2 = 20 {x}^{2} \\ \\ \sf \: 180 = 20 {x}^{2} \\ \\ \sf \: {x}^{2} = \cancel\frac{180}{20} \\ \\ \sf \: {x}^{2} = 9 \\ \\ \sf \: { \underline{ \underline{x = 3}}}$

Base = 4x

ㅤ ㅤ = 4(3)

ㅤ ㅤ= 12m

Base = 12m

_______________________

Height = 5x

ㅤㅤ ㅤ = 5(3)

ㅤ ㅤ ㅤ= 15m

Height = 15m

Hence , Base of the triangle is 12m and height is 15m.