The ratio of bases of two triangles is x: y a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the bases of the two triangles be $b_1$ and $b_2$,and their altitudes be $h_1$ and $h_2$ respectively.Given that the ratio of their bases is $

Vedclass · Accepted Answer

$a y: b x$

Vedclass · Answer

(C) Let the bases of the two triangles be $b_1$ and $b_2$,and their altitudes be $h_1$ and $h_2$ respectively.Given that the ratio of their bases is $\frac{b_1}{b_2} = \frac{x}{y}$ and the ratio of their areas is $\frac{\Delta_1}{\Delta_2} = \frac{a}{b}$.The area of a triangle is given by the formula $\Delta = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{altitude}$.Therefore,$\frac{\Delta_1}{\Delta_2} = \frac{\frac{1}{2} b_1 h_1}{\frac{1}{2} b_2 h_2} = \frac{b_1}{b_2} 	imes \frac{h_1}{h_2}$.Substituting the given values,we get $\frac{a}{b} = \frac{x}{y} 	imes \frac{h_1}{h_2}$.Solving for the ratio of altitudes $\frac{h_1}{h_2}$,we get $\frac{h_1}{h_2} = \frac{a}{b} 	imes \frac{y}{x} = \frac{ay}{bx}$.Thus,the ratio of their corresponding altitudes is $ay: bx$.

The ratio of bases of two triangles is $x: y$ and that of their areas is $a: b$. Then the ratio of their corresponding altitudes will be

Similar Questions

Find the area of a triangle in which base is $1.5\, m$ and height is $75\, cm$? (in $sq. cm.$)

What is the area of a given right-angled triangle?
$I.$ The length of the hypotenuse is $5\, cm$.
$II.$ The perimeter of the triangle is four times that of its base.
$III.$ One of the angles of the triangle is $60^{\circ}$.

If a diagonal of a square is doubled,how does the area of the square change?

The diameter of a circle is $105 \, cm$ less than its circumference. What is the diameter of the circle? (in $cm$)

The area of a triangle is $216 \, cm^{2}$ and its sides are in the ratio $3:4:5$. The perimeter of the triangle is ....... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module