For going to a city B from city A,there is a | vedclass

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

Question

(A) Given,$AC \perp CB$,$AC = 2x \, km$,$CB = 2(x+7) \, km$ and $AB = 26 \, km$.From the figure,we have a right-angled $	riangle ACB$ with the right

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) Given,$AC \perp CB$,$AC = 2x \, km$,$CB = 2(x+7) \, km$ and $AB = 26 \, km$.From the figure,we have a right-angled $	riangle ACB$ with the right angle at $C$.In $	riangle ACB$,by the Pythagoras theorem:$AB^2 = AC^2 + BC^2$$(26)^2 = (2x)^2 + \{2(x+7)\}^2$$676 = 4x^2 + 4(x^2 + 49 + 14x)$$676 = 4x^2 + 4x^2 + 196 + 56x$$676 = 8x^2 + 56x + 196$$8x^2 + 56x - 480 = 0$Dividing by $8$,we get:$x^2 + 7x - 60 = 0$$x^2 + 12x - 5x - 60 = 0$$x(x + 12) - 5(x + 12) = 0$$(x + 12)(x - 5) = 0$$x = -12$ or $x = 5$.Since distance cannot be negative,$x = 5$ (as $x 
eq -12$).Now,$AC = 2x = 2(5) = 10 \, km$ and $BC = 2(x+7) = 2(5+7) = 24 \, km$.The distance covered to reach city $B$ from city $A$ via city $C$ is $AC + BC = 10 + 24 = 34 \, km$.The distance covered to reach city $B$ from city $A$ after the construction of the highway is $AB = 26 \, km$.Therefore,the distance saved is $34 - 26 = 8 \, km$.

Similar Questions

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$,$M \in \overline{AD}$ and $N \in \overline{BC}$. If $\overline{MN} \parallel \overline{AB}$,prove that $\frac{DM}{MA} = \frac{CN}{NB}$.

$\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow EFD$. $AB : BC : CA = 4 : 3 : 5$. If the perimeter of $\Delta DEF$ is $36$,find the measures of all the sides of $\Delta DEF$.

In $\Delta ABC$,$A-N-B$,$A-M-C$ and $B-X-C$. $\overline{XM} \parallel \overline{AB}$ and $\overline{XN} \parallel \overline{AC}$. $\overline{MN}$ intersects $\overline{CB}$ at $T$. Prove that $TX^2 = TB \times TC$.

In rectangle $ABCD$,$AB + BC = 23$ and its area is $120$. If $AB > BC$,then $AB = \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module