Question

The altitude and base of a triangle having area 600 sq. cm are in ratio 25:3. Find the altitude and the base​

Answer 1

$\star \; {\underline{\boxed{\pmb{\purple{\frak{ \; Given \; :- }}}}}}$

• Ratio of Base and Height = 25:3
• Area of Triangle = 600 cm²

$\star \; {\underline{\boxed{\pmb{\pink{\frak{ \; To \; Find \; :- }}}}}}$

• Base and Height = ?

$\star \; {\underline{\boxed{\pmb{\green{\frak{ \; SolutioN \; :- }}}}}}$

~ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Triangle)}} = \dfrac{1}{2} \times Base \times Height }}}}}$

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~ Let the Ratios :

• Base = 25y
• Height = 3y

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~ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times Base \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 600 = \dfrac{1}{2} \times 25y \times 3y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 600 \times 2 = 1 \times {75y}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 1200 = {75y}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{1200}{75} = {y}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{1200}{75} = {y}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 16 = {y}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \sqrt{16} = y }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\red{\frak{ y = 4 }}}}}}}}$

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~ Calculating the Base and Height :

• Base = 3y = 3(4) = 12 cm
• Height = 25y = 25(16) = 100 cm

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~ Therefore :

❛❛ Base of the Triangle is 12 cm and its Height is 100 cm . ❜❜

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Answer 2

100 m and 12 m is the answer