Question

the base and the height of a triangle are in the ratio 4:5. if the area of the triangle is 40cm^2, find its base and height.
[let base be 4x m and height be 5x m.
Therefore 1/2 ×4x×5x=40] ​

Answer 1

A᭄nswer: Base = 8,Hight = 10

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Step-by-step explanation:

Given:

The base and the height of a triangle are in the ratio 4:5. If the area of the triangle is 40m²

To find:

its base and height.

Solution:

The base and the height of a triangle are in the ratio

=4:5

=4:5So,

=4:5So,Base=4x

=4:5So,Base=4xHeight=5x

=4:5So,Base=4xHeight=5xSince, area of the triangle =40 m²

½×4x×5x=40

×4x×5x=4020x² = 80

80x² = 4

4x = 2

2Therefore,

2Therefore,Base=4×2=8 m

2Therefore,Base=4×2=8 mHeight=5×2=10 m

Answer 2

Question:

The base and the height of a triangle are in the ratio 4:5. if the area of the triangle is 40cm² , find its base and height.

Given:

• The base and height of a triangle are in the ratio of 4:5

• Area of the traingle is 40 cm²

To Find:

• Base of the traingle

• Height of the traingle

Formula Used:

• Area of the traingle = 1/2 × Base × height

Solution:

In the question the hint is given. So according to the hint,

Let,

• Base of the traingle be 4x m

• Height of the traingle be 5x m

Applying the formula of Area of the traingle,

Area of the traingle = 1/2 × base × height

➦ 40 = 1/2 × 4x × 5x

➦ 40 = 2x × 5x

➦ 40 = 10x²

➦ 10x² = 40

➦ x² = 40/10

➦ x² = 4

➦ x = √4

➦ x = 2 m

Hence , we got the value of x which is 2 m

Now,

• Base of the traingle = 4x

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 4 × 2

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 8 m

• Height of the traingle = 5x

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 5 × 2

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 10 m

Hence,

• the Base of the traingle is 8 m

• the Height of the traingle is 10 m

Happy Learning!!