Question

Find the area of a right triangle
whose two sides are 24cm and 7cm and the
perimeter is 56cm.​

Answer 1

Answer :

• Area of triangle = 84 cm²

Given :

• Two sides of triangle are 24 cm and 7 cm
• Perimeter of triangle is 56 cm

To find :

• Area of right triangle = ?

Solution:

Let, third side of triangle be x

then, Since

→ Perimeter of Triangle = 56 cm

→ 24 cm + 7 cm + x  = 56 cm

→ 31 cm + x  = 56 cm

→ x = 56 cm - 31 cm

→ x = 25 cm

It means, Largest side of right angled triangle is 25 cm so it will be hypotenuse. Hence, Height and base of triangle are 24 cm and 7 cm.

so,

→ Area of triangle = 1/2 × base × height

→ Area of triangle = 1/2 × 7 cm × 24 cm

→ Area of triangle = 84 cm²

Therefore,

• Area of right angled triangle is 84 cm².

Answer 2

$\setlength{\unitlength}{1.9cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{B}}\put(10.6,1){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.6,0.7){\sf{\large{7 cm}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\put(7.4,1.8){\sf c}\put(9.4,2.2){\sf 24 cm}\end{picture}$

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${\underline{\frak{Given}}}\begin{cases} & \text{a = \bf{24\; cm}} \\ & \text{b = \bf{7 \;cm}} \\ & \text{Perimeter = \bf{ 56\; cm}} \end{cases}$

☯ We have to find, Area of right ∆.

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\purple{Perimeter_{\;\triangle} = a + b + c}}}}$

$\qquad\qquad\quad:\implies\sf 56 = 24 + 7 + c$

$\qquad\qquad\qquad:\implies\sf 56 = 31 + c$

$\qquad\qquad\qquad:\implies\sf 56 - 31 = c$

$\qquad\qquad\qquad:\implies{\boxed{\frak{\pink{c = 25}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hypotenuse\;of\;\triangle\;is\; \bf{25\;cm}}}}$

━━━━━━━━━━━━━━━━━━━━━

☯ Now, Finding area of right ∆,

${\underline{\frak{Here}}}\begin{cases} & \text{Hypotenuse = \bf{25 \;cm}} \\ & \text{Base = \bf{7\;cm}} \\ & \text{Perpendicular = \bf{24\; cm}} \end{cases}$

$\dag\;{\underline{\frak{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\purple{Area_{\;\triangle} = \dfrac{1}{2} \times base \times Height}}}}$

$\qquad\qquad\quad:\implies\sf \dfrac{1}{2} \times 7 \times 24$

$\qquad\qquad\qquad:\implies\sf \dfrac{1}{2} \times 168$

$\qquad\qquad\quad\quad:\implies{\boxed{\frak{\pink{84\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Area\;of\; right\;angled\; triangle\;is\; \bf{84\;cm^2}}}}$