Question

15. The hypotenuse of a rectangle is 5 cm and its length is 4 cm, find the area of
the rectangle​

Answer 1

QUESTION

The diagonal of a rectangle is 5 cm and its length is 4 cm, find the area of  the rectangle​.

                                                 

According to the Pythagorean theorem,

$\boxed{(Hypotenuse)^{2} = Side^{2} +side^{2} }$

∵Since each angle of a Δ is 90°

Given

Length of the rectangle =  4 cm

Substituting , we get,

$5^{2} = 4^{2} + Breadth^{2} \\25 = 16 + Breadth^{2} \\Breadth^{2} = 25-16 = 9\\=> Breadth = 3 \ cm$

Area of the rectangle = Length * breadth

                                     = 3 * 4

                                    = 12 cm²

$\boxed{\boxed{\bold{Therefore, \ Area \ Of \ The \ Rectangle \ Is \ 12 \ cm^{2}} }}$

                                                         

Answer 2

$\large{\underline{\boxed{\mathfrak\blue{Area \: of \: rectangle = 12 \: cm^2 }}}}$

*Reference of diagram given below:-

$\setlength{\unitlength}{0.78 cm}\begin{picture}(12,4)\thicklines\put(5.6,9.1){ A }\put(5.5,5.8){ B }\put(11.1,5.8){ C }\put(11.05,9.1){ D }\put(4.5,7.5){ 3\:cm }\put(8.1,5.3){ 4 \:cm }\put(11.5,7.5){ 3 \:cm }\put(8.1,9.5){ 4\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(6,6){\line(5,3){5}}\end{picture}$

Given:-

• Hypotenuse of rectangle = 5 cm
• Length = 4cm

To find:-

• Area of rectangle = ?

According to Pythagoras theorem:-

⇢ (Hypotenuse)² = Length² + Breadth²

⇢ 5² = 4² + Breadth²

⇢ 25 = 16 + Breadth²

⇢ Breadth² = 25 - 16

⇢ Breadth² = 9

⇢ Breadth = √9

⇢ Breadth = 3 cm

$\rule{100}2$

We know that,

$\star\:{\boxed{\mathfrak\red{Area\:of \: rectangle = Length \times Breadth}}}$

⇢ Area of rectangle = (4 × 3) cm²

⇢ Area of rectangle = 12 cm²

$\therefore{\underline{\rm{Area \: of \: rectangle = 12 \: cm^2}}}$