Question

the ratio of the length and the breadth of a rectangle is 4:3 and its area is 180 sq. cm, find its length..​

Answer 1

Answer

• Length of rectangle = 4√15 cm.
• Breadth of rectangle = 3√15 cm.

Given

• Ratio between the length and breadth of a rectangle is 4 : 3.
• Area of rectangle = 180 sq. cm.

To Find

• The length of the rectangle.

Step By Step Explanation

Assumption :

Let us assume that the length of the rectangle be 4x cm and breadth be 3x cm.

Formula Used :

$\bold{\underline{\boxed{\mathfrak{\green{Area_{(Rectangle)} = Length \times Breadth}}}}}$

Substituting the values :

Let's substitute the values in the above formula to find the length and breadth of the rectangle.

So let's do it !!

$\longmapsto\tt180 = 4x \times 3x \\ \\ \longmapsto\tt180 = 12 {x}^{2} \\ \\ \longmapsto\tt \cancel\cfrac{180}{12} = {x}^{2} \\ \\\longmapsto\tt 15 = {x}^{2} \\ \\\longmapsto\tt \sqrt{15} = x$

Length ⤵

$\sf4 \times \sqrt{15} \implies \red{4 \sqrt{15} \: cm}$

Breadth ⤵

$\sf3 \times \sqrt{15} \implies \purple{3 \sqrt{15} \: cm}$

Therefore, length of rectangle = 4√15 cm and breadth = 3√15 cm.

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