Question

A student was asked to measure the
length and breadth of a rectangle. By
mistake, he measured the length
20% less and the breadth 10% more. If its
original area is 200 sq cm, then find the
area after this measurement?​

Answer 1

Answer:

$\bigstar$ To Find:

⇒ area after this measurement

$\bigstar$ Solution:

Net effect on area = -20 + 10 + [(-20 )(10)/100] %

= $\sf {(-10 - 2) \% =\sf{ - 12\%}}$

$\boxed {\implies \sf {12\%}}$

After this mistake new area = (100 - 12)% of 200

$\sf {= \dfrac{88}{100} * 200}$

$\sf {= 176\; sq \;cm}$

Therefore, the area after this measurement is $\green{\boxed{\sf { 176\; sq \;cm}}}$

Answer 2

Given :

• A student was asked to measure the length and breadth of a rectangle. By mistake, he measured the length 20% less and the breadth 10% more.
• Original area of the rectangle = 200 cm².

To find :

• Area after measurement.

Solution :

Let the original length of the rectangle be x cm and the original breadth of the rectangle be y cm.

✪ Original area of rectangle is 200 cm² ✪

We know,

Area of rectangle = length× breadth

According to the question,

$\sf{xy=200.......(i)}$

✪By mistake, he measured the length 20% less and the breadth 10% more.✪

$\sf{Length=x-x\times\frac{20}{100}\:cm}$

$\implies\sf{Length=\frac{4x}{5}\:cm}$

$\sf{Breadth=y+y\times\frac{10}{100}\:cm}$

$\implies\sf{Breadth=\frac{11y}{10}\:cm}$

✪ Now find the area after measurement✪

$\sf{Area=length\times\: breadth}$

$\implies\sf{Area=\frac{4x}{5}\times\frac{11y}{10}\:cm^2}$

$\implies\sf{Area=\frac{22xy}{25}\:cm^2}$

★ Put xy = 200 from eq (i)★

$\implies\sf{Area=\frac{22\times\:200}{25}\:cm^2}$

$\implies\sf{Area=176\:cm^2}$

Therefore, the area after measurement is 176 m².