Similar Triangles: Finding Side Length YZ
The problem states that triangle ABC is similar to triangle XYZ ($\Delta ABC \sim \Delta XYZ$). A key property of similar triangles is that their corresponding sides are proportional.
This means the ratio of corresponding sides is constant:
$ \frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ} $
We are given the lengths:
- $AB = 4 \text{ cm}$
- $BC = 6 \text{ cm}$
- $XY = 8 \text{ cm}$
We need to find the length of YZ. Using the proportionality of the corresponding sides AB and XY, and BC and YZ, we can set up the equation:
$ \frac{AB}{XY} = \frac{BC}{YZ} $
Now, substitute the known values into the equation:
$ \frac{4 \text{ cm}}{8 \text{ cm}} = \frac{6 \text{ cm}}{YZ} $
Simplify the left side of the equation:
$ \frac{1}{2} = \frac{6 \text{ cm}}{YZ} $
To solve for YZ, we can cross-multiply:
$ 1 \times YZ = 2 \times 6 \text{ cm} $
$ YZ = 12 \text{ cm} $
Therefore, the length of YZ is 12 cm.
Similar Questions
- In an urban project, triangular plots with side ratios 3:4:5 are allocated. If the perimeter is 60 m, find the area.
- A right-angled triangle ABC has legs AB=6 cm and BC=8 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. What is the length of the altitude BD?
- If in $\Delta LMN$ and $\Delta OPQ$, $\angle L = \angle O$, $LM = OP$, and $\angle M = \angle P$, which rule proves $\Delta LMN \cong \Delta OPQ$?
- A triangle with all its angles less than $90^\circ$ has its Orthocenter located where?
- In triangle ABC, DE is drawn parallel to BC, intersecting AB and AC at D and E respectively. If AD=3, DB=6, and AE=4, find EC.
- Triangle PQR has vertices P(1, 1), Q(4, 1), and R(1, 5). Triangle STU has vertices S(6, 2), T(9, 2), and U(6, 6). Are these two triangles congruent?
- Two triangles, $\Delta PQR$ and $\Delta STU$, have $PQ=ST$, $PR=SU$, and $\angle QPR = \angle TSU$. By what rule are they congruent?
- The Incenter of a triangle is located at $(3, 4)$. The length of the altitude from the Incenter to side AB is $2\text{ units}$. What is the radius of the triangle's incircle?
- If in triangle ABC, $DE \parallel BC$ and $AD/DB = \frac{1}{2}$, and $AE = 5\text{ cm}$, then $EC$ is:
- For a triangle with one interior angle greater than 90°, where is its Orthocenter located?
Important Questions from Triangles, Congruence and Similarity
Angle between the internal bisectors of two angles ∠B and ∠C of a ΔABC is 132°, then the value of ∠A is
In ΔPQR, PQ = PR and S is a point on QR such that ∠PSQ = 96° + ∠QPS and ∠QPR = 132°. What is the measure of ∠PSR?
In Δ ABC, ∠A = 50°. If the bisectors of the angle B and angle C, meet at a point O, then ∠BOC is equal to:
Triangle ABC is right angled at B. BD is an altitude intersecting AC at D. If AC = 9 cm and CD = 3 cm. then find the measure of AB (in cm).
The base and altitude of an isosceles triangle are 10 cm and 12 cm respectively. Then the length of each equal side is:
