Question

plz give correct answer​

Answer 1

$\implies\huge \sf \underline \red{Answer}$

$\: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \pink{ \sf{ area = 96 {cm}^{2} }}}}}}$

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$\implies \huge \sf \underline\blue{Given : }$

• base and hypotenuse = 4: 5
• perimeter = 48

$\implies \sf \huge \underline \pink{To \: find : }$

• Area of triangle

$\implies \sf \huge \underline \orange{solution : }$

• let us take base and hypotenuse be 4x and 5x

$\star \sf \underline{ \: now \: take \: phytagoras \: theorem : }$

$\: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \sf{ {h}^{2} = {p}^{2} + {b}^{2} \: }}}}}}$

so,

hypotenuse is 4x

base is 5x

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies\sf{ {p}^{2} = {5x}^{2} - {4x}^{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf{ {p}^{2} = {25x}^{2} - {16x}^{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf{ {p} = { \sqrt{ {9}^{2} } }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf{ {p =3}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \sf{p = 3 \: }}}}}}$

we know that,

$\sf \implies{perimeter = sum \: of \: all \: sides}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \blue{3x + 4x + 5x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \blue{12x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \blue{given \: perimeter = 48}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \blue{12x = 48}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \blue{x = \dfrac{48}{12} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \blue{x = 4cm}$

Now,

$\star \sf \underline{putting \: the \: value \: of \: x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies{base = 4x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies{4(4) = 16cm}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies{hypotenuse = 5x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies{3(4) = 12cm}$

$\star \implies \sf \underline{now \: formula}$

we know that area of triangle formula,

$\: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \sf{ \dfrac{1}{2} \times base \times height \: }}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies{ \dfrac{1}{2} \times 16 \times 12 }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies{area = 96 {cm}^{2} }$

$\implies \sf \underline \purple{Area = 96 {cm}^{2}}$

Answer 2

Step-by-step explanation:

the ratio of base to hypotenuse

is 4:5, then the final side (upright)

will = 3. (3,4,5 triangle)

3+4+5 = 12

Perimeter = 48 cm

Base = 4/12 x 48

Base = 16 cm

Hypotenuse = 5/12 x 48

Hypotenuse = 20 cm

Upright = 3/12 x 48

Upright = 12 cm.

Area of a triangle

= 1/2(base x height)

=1/2(16 x 12)

= 96 cm^2