In triangle ABC, DE || BC. AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value x.

Expert Solution

In △ABC, we have DE || BC

Therefore

From Thales theorem, we know that the ratio of any two corresponding sides in two equiangular triangles is always the same. This theorem is called as Basic Proportionality Theorem

AD /DB = AE/ EC

AD × EC = AE × DB

On substituting the known values we get

x(x-1) = (x-2)(x+2)

x2 – x = x2 – 4

-x=-4

x = 4

The value of x =4.

Nikhil Thakur answered 2 years ago

In triangle ABC, cevians AD and CF are bisectors. Find area ABC / area AFD if...

In triangle ABC, cevians AD and CF are bisectors. Find area ABC / area AFD if AB = 21, AC = 28, and BC = 20.

For triangle ABC, the lines: - through A, parallel to BC; - through B, parallel to...

For triangle ABC, the lines: - through A, parallel to BC; - through B, parallel to AC; - through C, parallel to AB intersect to form a triangle. Prove that the triangle is similar to triangle ABC.

ABC is a right triangle. AM is perpendicular to BC. The size of the angle ABC is equal to 55 degrees.

ABC is a right triangle. AM is perpendicular to BC. The size of the angle ABC is equal to 55 degrees. Find the size of angle ACM.

Given triangle(ABC) with A-D-C, then BD < BA or BD < BC. Prove that the set...

Given triangle(ABC) with A-D-C, then BD < BA or BD < BC. Prove that the set consisting of a circle and its interior is a convex set.

DB 1- What is the time value of money? DB 2- What is the nature of...

DB 1- What is the time value of money? DB 2- What is the nature of interest? Distinguish between “simple interest” and “compound interest.” DB 3- What are the primary characteristics of an annuity? Differentiate between an “ordinary annuity” and an “annuity due.

Find the absolute maximum value and the absolute minimum value of the function f(x,y) = (1+x^2)(1−y^2)...

Find the absolute maximum value and the absolute minimum value of the function f(x,y) = (1+x^2)(1−y^2) on the disk D = {(x,y) | x2+y2⩽1}?

solve the SDE dX = − 1 /τ( (X − µ)dt) + (2D)-1/2 dB. X(t =...

solve the SDE dX = − 1 /τ( (X − µ)dt) + (2D)-1/2 dB. X(t = 0) = β

A particle's wave function is ψ(x) = Ae−c(x−b)2 where A = 1.95 nm−1/2 and b =...

A particle's wave function is ψ(x) = Ae−c(x−b)2 where A = 1.95 nm−1/2 and b = 0.600 nm. (a) What is the value of the constant c (in nm−2)? nm−2 (b) What is the expectation value for the position of this particle (in nm)? nm

45. If the area model for a triangle is A = 1/2 bh, find the area...

45. If the area model for a triangle is A = 1/2 bh, find the area of a triangle with a height of 16 in. and a base of 11 in.? the answer should be A=88 in.squier 43. Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of 60 mi/h for 6.75 h.? the answer should be 405 mi 47. Use the formula from the previous question to find...

Find the average value of f(x, y) = e −(x 2+y 2 ) on x 2...

Find the average value of f(x, y) = e −(x 2+y 2 ) on x 2 + y 2 ≤ π

Question