4. DEFG and ABCD are similar figures. $DE=12cm$, $EF=xcm$, $EG=15cm$, $GD=10cm$, $AB=8cm$, $BC=5cm$, $CD=mcm$ and $DA=ncm$. Calculate the values of x, m and n. - Noon Academy

4. DEFG and ABCD are similar figures. $DE=12cm$ , $EF=xcm$ , $EG=15cm$ , $GD=10cm$ , $AB=8cm$ , $BC=5cm$ , $CD=mcm$ and $DA=ncm$ . Calculate the values of x, m and n.

Class 10 | Frank | ICSE | Maths | Similarity

4. DEFG and ABCD are similar figures. $DE=12cm$ , $EF=xcm$ , $EG=15cm$ , $GD=10cm$ , $AB=8cm$ , $BC=5cm$ , $CD=mcm$ and $DA=ncm$ . Calculate the values of x, m and n.

Given, quadrilateral DEFG $\sim$ quadrilateral ABCD. $DE=12cm$ , $EF=xcm$ , $FG=15cm$ , $GD=10cm$ , $AB=8cm$ , $BC=5cm$ , $CD=mcm$ and $DA=ncm$ .

$DE/AB=EF/BC=FG/DC=GD/DA$

$12/8=x/5=15/m=10/n$

Consider, $12/8=x/5$

By cross multiplication,

$12\times 5=8\times x$

$60=8x$

$x=60/8$

$x=7.5cm$

Then, consider $x/5=15/m$

$7.5/5=15/m$

By cross multiplication we get,

$7.5\times m=15\times 5$

$7.5m=75$

$m=75/7.5$

$m=750/75$

$m=10cm$

Now, consider $15/m=10/n$

$15/10=10/n$

By cross multiplication we get,

$15\times n=10\times 10$

$15n=100$

$n=100/15$

$n=6.67cm$

Hence, value of x is $7.5cm$ , value of m is $10cm$ and value of n is $6.67cm$ .

i

More Material

A …… lens is used to correct myopia and a ….. lens is used to correct hypermetropia.
A Concave, concave
B Convex, convex
C Convex, concave
D Concave, convex

Rate of reaction of any substance depends on
(A) active mass
(B) molecular weight
(C) atomic weight
(D) equivalent weight

Formula of oleum is
(A) $\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{7}$
(B) $\mathrm{H}_{2} \mathrm{SO}_{4}$
(C) $\mathrm{H}_{2} \mathrm{SO}_{3}$
(D) $\mathrm{H}_{2} \mathrm{SO}_{5}$

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

Two cells of emf $\varepsilon_{1}$ and $\varepsilon_{2}$ , internal resistance $r_{1}$ and $r_{2}$ , connected in parallel. The equivalent emf of the combination is- (A) $\frac{\varepsilon_{1} r_{1}+\varepsilon_{1} r_{1}}{r_{1}+r_{2}}$ (B) $\frac{\varepsilon_{1} r_{2}+\varepsilon_{2} r_{1}}{r_{1}+r_{2}}$ (C) $\sqrt{\varepsilon_{1} \times \varepsilon_{2}}$ (D) $\frac{\varepsilon_{1}+\varepsilon_{2}}{2}$

If the points $A(a, 0), B(0, b)$ and $C(1,1)$ are collinear, prove that $\frac{1}{a}+\frac{1}{b}=1$

If $A(-2,0), B(0,4)$ and $C(0, k)$ be three points such that area of a $A B C$ is 4 sq units, find the value of $k$ .

Find the value of $k$ for which the area of a ABC having vertices $A(2,-6), B(5,4)$ and $C(k, 4)$ is 35 sq units.

Find the value of $k$ for which the points $A(1,-1), B(2, k)$ and $C(4,5)$ are collinear.

Find the value of $k$ for which the points $P(5,5), Q(k, 1)$ and $R(11,7)$ are collinear.

Find the value of $k$ for which the points $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear.

Use determinants to show that the following points are collinear. $P(-2,5), Q(-6,-7)$ and $R(-5,-4)$

← Previous Next →