Question

The base & height of a triangle are in the ratio 8:5 & its area is 320cm². Find the height & base

of the triangle.h

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Answer 1

Answer:

The answer is given in the attachment.

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Step-by-step explanation:

Answer 2

• The base of a triangle = 32 cm.
• The height of a triangle = 20 cm.

Given :–

• The base and height of a triangle in the ratio = 8 : 5.
• Area of a triangle = 320 cm².

To Find :–

• The height and the base of a triangle.

Solution :–

Let,

The base of a triangle be 8x.

The height of a triangle be 5x.

Given that,

Area of a triangle = 320 cm²

$\boxed{\dfrac{1}{2} \times b \times h = 320 \: {cm}^{2} }$

Here,

• Base = b = 8x.
• Height = h = 5x.

Now,

$\hookrightarrow \dfrac{1}{2} \times 8x \times 5x = 320 \: {cm}^{2}$

$\hookrightarrow {40x}^{2} = 320 \times 2 \: {cm}^{2}$

$\hookrightarrow {40x}^{2} = 640 \: { cm}^{2}$

$\hookrightarrow {x}^{2} = \cancel\dfrac{640}{40} \: {cm}^{2}$

$\hookrightarrow {x} = 16 \: {cm}^{2}$

$\hookrightarrow x = 4 \: cm$

Now, we have to find the base and the height of a triangle.

So,

Base = 8x = 8 × 4 cm = 32 cm.

Height = 5x = 5 × 4 cm = 20 cm.

Hence,

The base and the height of a triangle is 32 cm and 20 cm.

Verification :–

• Area of a triangle = 320 cm²
• Base = 32 cm.
• Height = 20 cm.

$\boxed{\dfrac{1}{2} \times b \times h = 320 \: {cm}^{2}}$

$\hookrightarrow\dfrac{1}{\cancel{2}} \times 32 \: cm \times \cancel{20} \: cm= 320 \: {cm}^{2}$

$\hookrightarrow 32 \: cm \times 10 \: cm = 320 \: {cm}^{2}$

$\hookrightarrow 320 \: {cm}^{2} = 320 \: {cm}^{2}$

Hence Verified !!