Question

Please explain properly.
Best answer will be marked brainliest.

Answer 1

Step-by-step explanation:

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Base=20\:cm}}}$

$\green{\tt{\therefore{Altitude=12\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Altitude \: of \: triangle = \frac{3}{5} th \: of \: corresponding \: base \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Base = ? \\ \\ \tt: \implies Altitude = ?$

• According to given question :

$\tt \circ \: Let \: Base \: be \: x \\ \\ \tt \circ \: Altitude \: = \frac{3}{5}x \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times b \times h \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times x \times \frac{3}{5} x \\ \\ \tt: \implies Area \: of \: triangle = \frac{3}{10} {x}^{2} \\ \\ \bold{As \: per \: given \: relation} \\ \tt \circ \: Base = x + 10 \\ \\ \tt \circ \: Altitude = \frac{3}{5} x - 4 \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times (x + 10 ) \times (\frac{3}{5} x - 4) \\ \\ \tt: \implies \frac{3}{10} {x}^{2} = \frac{1}{2} \times (x + 10) \times ( \frac{3}{5} x - 4) \\ \\ \tt: \implies \frac{3}{5} {x}^{2} = \frac{3}{5}{x}^{2} - 4x + 6x - 40 \\ \\ \tt: \implies \frac{3}{5} {x}^{2} - \frac{3}{5 } {x}^{2} = 2x - 40 \\ \\ \tt: \implies 2x = 40 \\ \\ \tt: \implies x = \frac{40}{2} \\ \\ \green{\tt: \implies x = 20 \: cm} \\ \\ \green{\tt \therefore Base \: is \: 20 \: cm} \\ \\ \green{\tt \therefore Altitude \: is \: 12 \: cm}$