Question

The length of a rectangle is 8 cm and each of its diagonals measure 10 cm. Find its breadth.​

Answer 1

Step-by-step explanation:

Let ABCD be the given rectangle in which length AB=8cm and diagonal AC=10cm

We have ∠ABC=90∘

AC2=AB2+BC2

BC2=AC2−AB2

={(10)2−(8)2}

=(100−64)

=36

Hence breadth =6cm

BC=36−−√

=6cm

Answer : 6cm

Answer 2

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

• The length of the rectangle = 8 cm
• The diagonal measures = 10 cm

$\huge{\underline{\underline{\bf{TO\:FIND:-}}}}$

Find the breadth of the rectangle = ?

$\huge{\underline{\underline{\bf{FORMULA\:USED:-}}}}$

$\large{\boxed{\bf{\green{{(Hypotenuse)}^{2}= {(base)}^{2} + {(perpendicular)} ^{2}}}}}$

$\huge{\underline{\underline{\bf{SOLUTION:-}}}}$

In ∆ ACD, We have given the hypotenuse = 10 cm and Base = 8 cm

We have to find the Perpendicular,

Putting the given values in the formula, we get

$\bf{{(Hypotenuse)}^{2}= {(base)}^{2} + {(perpendicular)} ^{2}}$

$\longrightarrow$$\bf{{(10)}^{2} = {(8)}^{2} + {(perpendicular)} ^{2}}$

$\longrightarrow$$\bf{{(perpendicular)} ^{2}={(10)}^{2} - {(8)}^{2} }$

$\longrightarrow$$\bf{{(perpendicular)} ^{2}=100 - 64 }$

$\longrightarrow$$\bf{{(perpendicular)} ^{2}=36}$

$\longrightarrow$$\bf{perpendicular=\sqrt{36}}$

$\longrightarrow$$\large\bf\green{perpendicular=6\: cm}$

Thus, the breadth of the rectangle is 6 cm

$\large{\underline{\underline{\bf{FINAL\:ANSWER:-}}}}$

$\huge{\boxed{\boxed{\bf{\green{BREADTH = 6\: cm}}}}}$

$\huge{\underline{\underline{\bf{VERIFICATION:-}}}}$

Putting the values in the formula

$\bf{{(Hypotenuse)}^{2}= {(base)}^{2} + {(perpendicular)} ^{2}}$

$\longrightarrow$$\bf{{(10)}^{2} = {(8)}^{2} + {(6)} ^{2}}$

$\longrightarrow$$\bf{100 = 64 + 36}$

$\longrightarrow$$\large\bf{100 = 100}$

$\longrightarrow$$\bf{[L.H.S. = R.H.S.]}$

$\huge{\underline{\underline{\bf{\green{VERIFIED...}}}}}$