Question

A string of length 100cm was fitted diagonally in A rectangular frame. if the breadth of theframe is 28cm.find its length.
​

Answer 1

Answer:

96

Step-by-step explanation:

Pythagoras Theorem

100²=28²+x²

x²=10000-784

x²=9216

x=96

Please mark as brainliest

Answer 2

Given:- Length of string is 100cm and breadth of rectangle is 28cm.

To find:- Length of the rectangle.

Solution :-

Let's assume that length of the

rectangle is x cm.

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\multiput(0,0)(0,2){2}{\line(1,0){3}}\multiput(0,0)(3,0){2}{\line(0,1){2}}\qbezier(0,0)(0,0)(3,2)\put(1,-0.3){ \bf x \ cm }\put(3.1,1){ \bf 28\ cm }\put(-0.2,-0.3){ \bf D }\put(3,-0.3){ \bf C }\put(-0.2,2.1){ \bf A }\put(3,2.1){ \bf B }\end{picture}$

We know that opposite sides of rectangle are equal. So, breadth = AD = BC = 28cm.

We also know that, angles between two adjacent sides of rectangle are 90°.

In ∆ADC, by applying pythagoras theorem,

$\sf \implies \: \: AC {}^{2} = AD {}^{2} + CD {}^{2} \\ \sf\implies (100cm) {}^{2} = (28cm) {}^{2} + CD {}^{2} \\ \sf\implies CD {}^{2} = 10000 - 784 \: cm {}^{2} \\ \sf\implies \: CD = \sqrt{9216} cm \\ \implies\boxed{ \purple{\bf\: CD = 96cm}}$

CD = length of rectangle.

Therefore, length of rectangle is 96cm.