Question

the base of the first triangle is equal to the base of the second triangle if their respective height are 10 cm and 14 cm findout ratio of the area​

Answer 1

Answer:

5 : 7

Step-by-step explanation:

Given :

• $\sf{Base_1\:=\:Base_2}$
• $\sf{h_1\:=\:10\:cm}$
• $\sf{h_2\:=\:14\:cm}$

To find :

• $\sf{\dfrac{Area_1}{Area_2}}$ = ?

Solution :

We know, area of a triangle = $\sf{\dfrac{1}{2}bh}$

Where, b = base of triangle

$\:\:\:\:\:\:\:\:\:\:$ h = height of triangle

$\implies\sf{\dfrac{A_1}{A_2}\:=\:\dfrac{\:\cancel{½}\:\times\:b_1\:\times\:h_1}{\:\cancel{½}\:\times\:b_2\:\times\:h_2}}$

[ $\because\:\sf{b_1\:=\:b_2,\:they\:will\:cancel\:out,\:½\:will\:also\:cancel\:out\:and\:put\:values\:of\:h_1\:and\:h_2 }$ ]

$\implies\:\sf{\dfrac{A_1}{A_2}\:=\:\dfrac{\cancel{b_1}\:\times\:10}{\cancel{b_2}\:\times\:14}}$

$\implies\:\sf{\dfrac{A_1}{A_2}\:=\:\dfrac{10}{14}}$

$\implies\:\sf{\dfrac{A_1}{A_2}\:=\:\dfrac{5}{7}}$

$\therefore$ Ratio of their areas is 5 : 7.